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brilliant n.  and  emirpimes

First numbers that belong to both sets:

15, 49, 143, 169, 187, 221, 289, 319, 341, 437, 493, 533, 551, 559, 589, 629, 667, 781, 817, 851, 871, 893, 899, 913, 923, 961, 1027, 1067, 1079, 1121, 1219, 1247, 1273, 1343, 1357, 1387, 1411, 1513, 1577, 1679, 1691, 1769, 1817, 1843, 1849, 1891, 1927, 1961, 2021, 2047, 2059, 2077, 2231, 2257, 2263, 2279, 2449, 2479, 2491, 2627, 2881, 3007, 3053, 3071, 3139, 3403, 3431, 3481, 3589, 3599, 3713, 3721, 3869, 4171, 4183, 4187, 4307, 4399, 5041, 5141, 5329, 5561, 5893, 5917, 5963, 6499, 6887, 6889, 7081, 7387, 7663, 10807, 11413, 11449, 11663, 11881, 12091, 12317, 12769, 13589, 13843, 14017, 14111, 14873, 15049, 15347, 15553, 15707, 15857, 15943, 16129, 16171, 16241, 16837, 16867, 17063, 17161, 17441, 17869, 18203, 18437, 18511, 18643, 18769, 19043, 19153, 19511, 19549, 19879, 19939, 20291, 20687, 20701, 20711, 20989, 22261, 22331, 22499, 22657, 22663, 22987, 24047, 24289, 24307, 24503, 24823, 24881, 24883, 24931, 26219, 26269, 26329, 26471, 26569, 26671, 26969, 26989, 28013, 28103, 28363, 28459, 28531, 28783, 28829, 28891, 28907, 28943, 30227, 30281, 30353, 30397, 30551, 30607, 30629, 30929, 30967, 31007, 31411, 31439, 31553, 31571, 31753, 31831, 31921, 31937, 31979, 32041, 32231, 32639, 32651, 32743, 32761, 32881, 33017, 33109, 33127, 33221, 33389, 33499, 33667, 33919, 34163, 34387, 34571, 34579, 34691, 34889, 35011, 35179, 35209, 35263, 35501, 35611, 35723, 35909, 35941, 35947, 36019, 36079, 36089, 36287, 36349, 36359, 36481, 36503, 36581, 36733, 36977, 37001, 37067, 37241, 37343, 37399, 37403, 37669, 37771, 37801, 37823, 37837, 37909, 37949, 38021, 38293, 38407, 38413, 38477, 38497, 38807, 38809, 38911, 39037, 39131, 39211, 39283, 39289, 39337, 39407, 39437, 39449, 39751, 39911, 41311, 41449, 41471, 41747, 41869, 41891, 43139, 43157, 43273, 43361, 43423, 43507, 43621, 43739, 43763, 43931, 43957, 45151, 45499.

Some larger examples :